A question about RSA key generation algorithm

Question

I'm fairly new to this stuff so be forgiving. I'm trying to learn how RSA works, My resources for the manner of sake:

• this video
• this wikipedia page

This is what I got so far:

since

$m^{phi(n)} \equiv 1 \bmod n$

as long as $m$ coprimes to $n$.

So eventually:

$m^{k * phi(n)+1} \equiv m \bmod n$

Now we construct $e$ and $d$:

$k*phi(n) +1 = e * d$

$e$ is selected so that it coprimes with $phi(n)$

I have 2 questions:

1. Since $m$ can be anything (this is the encrypted content right?), how do you verify that $m$ and $n$ coprimes, as needed for the Euler's theorom to work?

2. Why do $e$ needs to comprime to $phi(n)$ ?

Thanks!